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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 13872.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13872.y1 | 13872m3 | \([0, 1, 0, -217424, 38785716]\) | \(22994537186/111537\) | \(5513691204716544\) | \([4]\) | \(147456\) | \(1.8689\) | |
| 13872.y2 | 13872m2 | \([0, 1, 0, -20904, -125244]\) | \(40873252/23409\) | \(578597225186304\) | \([2, 2]\) | \(73728\) | \(1.5223\) | |
| 13872.y3 | 13872m1 | \([0, 1, 0, -15124, -719428]\) | \(61918288/153\) | \(945420302592\) | \([2]\) | \(36864\) | \(1.1758\) | \(\Gamma_0(N)\)-optimal |
| 13872.y4 | 13872m4 | \([0, 1, 0, 83136, -915948]\) | \(1285471294/751689\) | \(-37158799573075968\) | \([2]\) | \(147456\) | \(1.8689\) |
Rank
sage: E.rank()
The elliptic curves in class 13872.y have rank \(0\).
Complex multiplication
The elliptic curves in class 13872.y do not have complex multiplication.Modular form 13872.2.a.y
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
